How long does it take torn tendons in the foot to heal naturally without surgery?

One must keep . In mind "natural" is not necessarily better. If the proximal portion of the tendon retracted then the tendon may never function optimally again. Only allow a tendon to heal naturally, if under the guidance and or consulting of a treating physician.
Months. Could take months depending on how severe the injury is.
Torn tendon. As dr kass said , natural is probably not the best way. A truly torn tendon need to be reapproximated surgically or you risk , as said, that tendon not working again. See your podiatrist for help.